1. Field of the Invention
The present invention relates generally to a charged particle beam exposure method, more particularly, to a charged particle beam exposure method performing a proximity effect correction in preparation of exposure data for a charged particle beam exposure apparatus in order to improve size accuracy of a transferred pattern, and a method for converting a rectangular pattern data of a charged particle beam exposure mask pattern to a lattice pattern data thereof in order to reduce an exposure dose for a relatively large pattern and a charged particle beam exposure method using the conversion method.
2. Description of the Related Art
In a case where a resist film on a substrate is irradiated with a charged particle beam, for example an electron beam, to draw a circuit pattern thereon, an electron beam incident on the resist film is partly scattered forward and the electron beam transmitted through the resist film is partly scattered backward to again impinge on the resist film. For this reason, even if an electron beam impinges at one point on the resist film, an influence thereof spreads around, causing a so-called proximity effect.
An energy intensity distribution (EID) function f (X, Y) on a resist film when an electron beam impinges at a point of X=0 and Y=0 on the resist film is expressed by the following equation in which a forward scattering term and a backscattering term approximate respective Gaussian functions:                               f          ⁡                      (                          X              ,              Y                        )                          =                              1                          π              ⁢                              xe2x80x83                            ⁢                              (                                  1                  +                  η                                )                                              ⁢                      {                                                            1                                      β                    f                    2                                                  ⁢                                  exp                  ⁡                                      (                                          -                                                                                                    X                            2                                                    +                                                      Y                            2                                                                                                    β                          f                          2                                                                                      )                                                              +                                                η                                      β                    b                    2                                                  ⁢                                  exp                  ⁡                                      (                                          -                                                                                                    X                            2                                                    +                                                      Y                            2                                                                                                    β                          b                          2                                                                                      )                                                                        }                                              (        1        )            
wherein xcex7 denotes a backscattering coefficient, xcex2f denotes a forward scattering radius and xcex2b denotes a backscattering radius. The values are dependent on energy of an electron beam, a thickness of a resist film, material of a substrate and others, each being determined by an experiment. With increase in acceleration voltage of the electron beam, xcex2f decreases and xcex2b increases.
In a prior art proximity effect correction method, fixed sample points were set at the middle points of sides or corners of each pattern to be exposed and an exposure intensity at each of the fixed sample points when pattern was exposed was calculated using the equation (1) and an exposure dose was determined such that the sum of the squares of differences each between an exposure intensity and a corresponding target value over all the fixed sample points is minimized.
However, in company with a progress in integration to a high degree of LSI, a rapid increase has occurred in the number of patterns, resulting in an excessively extended calculation time.
Hence, there has been a desire for a proximity effect correction method capable of reducing the calculation time and confining size error of a developed pattern (transferred pattern) within an allowable range.
As one of such methods, there has been disclosed a method in, for example, JP No. 2502418 and Journal of Vacuum Science Technology, Vol. B10, No. 6, pp. 3072-3076, 1992; in which method a layout plane of an LSI exposure pattern is divided into squares in mesh and a pattern area density is calculated for each of the squares to thereby obtain an approximate value of a scattering exposure intensity of a square of interest in consideration of influences of peripheral squares on the square of interest on the basis of the backscattering term of the equation (1). In this method, an exposure dose is determined such that the sum of the half value of a peak of a forward scattering intensity and a backscattering intensity is constant.
According to the method, using a simple and easy-to-use algorithm, it is possible to prevent a global variation in size of a transferred pattern caused by an influence of backscattering.
However, since no consideration is given to a spread of absorbed energy distribution due to forward scattering, it is not guaranteed that a size of a transferred pattern is equal to a design width. That is, as pattern elements become finer, a spread of an absorbed energy distribution at a half value intensity cannot be neglected, thereby making a size of a transferred pattern larger than a design width due to forward scattering.
Therefore, a proximity effect correction method as described below is proposed in JP 11-151330 A.
(A) A pattern width is adjusted such that a half-width of a forward scattering intensity distribution, determined by surface integration of the forward scattering term of the energy intensity distribution function over a pattern of interest, is equal to a design width and a forward scattering intensity xcex5p giving the half-width is determined as a reference forward scattering intensity;
(B) an exposure intensity xcex1pxc2x7xcex7 due to the backscattering term of the energy intensity distribution function is determined using a pattern area density map method; and
(C) a corrected exposure dose Qcp is determined such that Qcp times (xcex5p+xcex1pxc2x7xcex7) is equal to a threshold value Eth of pattern developing.
For example, when, as shown by dotted lines in FIG. 51(A), design widths in the X direction of a large width pattern and a small width pattern are (X2xe2x88x92X1) and (X4xe2x88x92X3), respectively, the pattern widths are narrowed as shown by solid lines in FIG. 51(A) in the processing of the above step (A). The large width pattern has xcex5p=xc2xd and xcex1p=1 and a pattern having such values is referred to as a reference pattern. If corrected exposure doses Qcp of the large width pattern and the small width pattern are expressed by Q1 and Q2, respectively, the following equation holds in the step (C):
(xc2xd+xcex7)Q1=(xcex5p+xcex1pxc2x7xcex7)Q2
where Q1 greater than Q2.
When the rectangular regions 13 and 14 shown by dotted lines, surrounding the rectangular transmission holes 11 and 12 shown by solid lines on the mask 10, are irradiated with an electron beam at respective exposure doses Q1 and Q2, an exposure intensity distribution on a wafer coated with a photoresist is determined as shown in FIG. 51(B).
According to this method, since a slant at the threshold value Eth of an exposure intensity distribution of each of the patterns is sharp, a variation in pattern width relative to a variation in exposure condition decreases, enabling to achieve a high accuracy pattern. Further, a corrected exposure dose can be determined in relatively short time. However, since the above method obtains a corrected exposure dose Qcp for each pattern, it cannot be applied in a case where a block exposure pattern in a small region of, for example, 4.5xc3x974.5 xcexcm2 on a stencil mask is selected to collectively expose.
Therefore, in JP 12-166465 A, the minimum value of corrected exposure doses for respective patterns in a block exposure pattern is determined as a corrected exposure dose Qcp for the block exposure pattern, and then auxiliary exposure is applied to exposure intensity-short regions in the block.
For example, when the rectangular transmission holes 11 and 12 of FIG. 51(A) are irradiated with an electron beam at an exposure dose Q1, covering a rectangular region 15 shown by a dotted line in FIG. 52(A), an exposure intensity distribution on a wafer coated with a photoresist is determined as shown in FIG. 52(B). In this state, the narrow line pattern cannot be developed due to shortage of exposure. Then, a rectangular transmission hole not shown for auxiliary exposure (ghost exposure) is irradiated with an electron beam to determine an exposure intensity distribution shown by an alternate long and short dash line in FIG. 53, thereby enabling developing of the narrow line pattern having a width (X4xe2x88x92X3).
As is apparent by comparison of FIG. 53 with FIG. 51(B), however, since a slant of an exposure intensity distribution at a pattern edge of a narrow line pattern is gentle, a variation in width of a transferred pattern image relative to a variation in exposure condition increases, causing reduction in pattern accuracy.
Further, since in the above method it is fundamental to calculate a corrected exposure dose for each pattern and, for example, the above problem arises even in block exposure of 4.5xc3x974.5 xcexcm2, the method cannot be applied to an electron projection lithography (EPL) in which a large region of, for example, 250xc3x97250 xcexcm2 on a wafer is collectively exposed.
In a case of an individual pattern exposure, a deviation between a design size and a completion size caused by the proximity effect can be corrected by optimizing a pattern size on a mask and an exposure dose in each design pattern. In a case where many patterns are collectively exposed, however, no optimization of an exposure dose in each pattern can be performed. Further, in a case where a correction for a proximity effect is performed by alteration in pattern size on a mask without altering an exposure dose, there was a problem that the correction is less effective and insufficient for a large pattern with a higher backscattering intensity.
Therefore, as for a large pattern, a method has been proposed that a pattern is converted to a lattice pattern to thereby reduce an effective exposure dose (JP Publication No. 11-329948-A).
However, this method employing the lattice pattern causes shortage of exposure, in result of forming an exposure-short region in an irregular shape on a resist pattern. This problem can be avoided by reducing a pattern subshape width and increasing the number thereof at the same pattern area density, but there arises a problem that as the pattern subshape width is smaller, size accuracy of a mask pattern is deteriorated.
Further, in a case where a lattice pattern is divided into two mask patterns complementary to each other, when one of the masks is switched to the other in exposure operation, relative shift in position occurs to thereby increase a distance between pattern subshapes, with the result that an irregular shape of an exposure-short region occurs.
Accordingly, it is an object of the present invention to provide a charged particle beam exposure method using a proximity effect correction method capable of, with a simple construction, reducing a variation in size of a transferred pattern obtained by small region collective exposure.
It is another object of the present invention to provide a charged particle beam exposure method using a proximity effect correction method capable of, with a simple construction, reducing a variation in size of a transferred pattern to a lower level even in a case where a large region is collectively exposed by a charged particle projection method.
It is another object of the present invention to provide a rectangle/lattice data conversion method for a charged particle beam exposure mask pattern capable of securing size accuracy of a mask pattern without generating an exposure-short region and a charged particle beam exposure method using the same conversion method.
It is still another object of the present invention to provide a rectangle/lattice data conversion method for a charged particle beam exposure mask pattern capable of avoiding generation of an exposure-short region even if a relative shift in position occurs when one of the masks complementary to each other is switched to the other and a charged particle beam exposure method using the conversion method.
In another aspect of the present invention, there is provided a charged particle beam exposure method with performing proximity effect correction by adjusting widths of patterns included in a block pattern, formed on a mask, for being repeatedly used and for collectively exposing, and by calculating a corrected exposure dose, the method comprising the steps of:
(a) determining a reference forward scattering intensity on the basis of a forward scattering intensity distribution of a pattern having a minimum design width included in the block pattern;
(b) adjusting each pattern width in the block pattern such that a width of a forward scattering intensity distribution at the reference forward scattering intensity becomes equal to a corresponding design width; and
(c) determining the corrected exposure dose such that, in regard to each pattern in the block pattern, a value obtained by multiplying a sum of the reference forward scattering intensity and a backscattering intensity by the corrected exposure dose becomes substantially equal to each other.
With this configuration, since the reference forward scattering intensity is determined on the basis of the forward scattering intensity distribution of the pattern having the minimum width included in the block pattern, a slant at a threshold value Eth of an exposure intensity distribution of a small width pattern can be sharp to thereby decrease a variation in width of a transferred pattern image relative to a variation in exposure condition, enabling to achieve a small width pattern with high accuracy. As for a large width pattern, although a slant of the forward scattering intensity distribution at an exposure intensity giving a design width is gentler than in a case where a reference forward scattering intensity is determined on the basis of the forward scattering intensity distribution, reduction in size accuracy is small because of having a large width. Therefore, relative size accuracy of a transferred pattern image is improved as a whole in comparison with the prior art.
Further, an algorithm for proximity effect correction is relatively simple.
In the step (a), for example, the reference forward scattering intensity is determined as equal to such a slice level that, in regard to the pattern having the minimum design width, by adjusting a width of the forward scattering intensity distribution at the slice level that is a predetermined percentage with respect to a peak value of the forward scattering intensity distribution, for example, a value in the range of 30 to 70%, becomes equal to a design width of the pattern.
Since a margin for a variation in size is small due to an influence of overlapping of exposure intensity distributions of adjacent patterns when the predetermined percentage is lower than 30% and due to a gentle slant of a forward scattering intensity distribution at the positions of the slice level when the predetermined percentage is higher than 70%, the effect of the present invention can be attained when the predetermined percentage is in the range of 30 to 70%.
In the step (c), for example, the corrected exposure dose Qcp is determined such that Qcp(xcex5p+xcex1pxe2x80x2xc2x7xcex7)=Eth holds, where xcex5p is the reference forward scattering intensity, Eth is a threshold value for pattern developing, xcex7 is a backscattering coefficient, and xcex1p is an effective pattern area density.
The step (b) comprises, for example, the steps of:
setting fixed sample points each being at a middle point on each side of each pattern in the block pattern; and
in regard to each of the fixed sample points, to adjust the pattern width, shifting a side corresponding to the fixed sample point in a direction perpendicular thereto such that an intensity of the forward scattering intensity distribution at the fixed sample point becomes equal to the reference forward scattering intensity.
As the width of a pattern becomes finer, a distance between patterns becomes shorter and when the distance becomes the order of an effective forward scattering radius xcex2fxe2x80x2, there arise influences of forward scattering from patterns in the neighborhood. However, the influences are taken into consideration for each of sides according to the above construction, enabling improvement on accuracy in a transferred pattern image.
The step (b) comprises, for example, the steps of:
dividing at least one pattern in the block pattern into plurality of rectangles;
setting fixed sample points each being at a middle point on a side, which is in contact with a boundary of the at least one pattern, of ones of the rectangles; and
in regard to each of the fixed sample points, to adjust the pattern width, shifting a side corresponding to the fixed sample point in a direction perpendicular thereto such that an intensity of the forward scattering intensity distribution at the fixed sample point becomes equal to the reference forward scattering intensity.
With this configuration, since the divided rectangles are each regarded as design patterns and each divided pattern width is adjusted, improvement is achieved on size accuracy of a transferred pattern.
In another aspect of the present invention, there is provided a charged particle beam exposure method with performing proximity effect correction by adjusting widths of a plurality of patterns of a mask for collectively exposing by a charged particle projection method, the method comprising the steps of:
(a) selecting a representative pattern from the plurality of patterns to determine a reference exposure intensity Eth on the basis of the representative pattern;
(b) determining a backscattering intensity distribution Fb of the plurality of patterns;
(c) adjusting a pattern width W of each pattern such that a width of a forward scattering intensity distribution at a slice level (Ethxe2x88x92Fb) becomes equal to a design width W0i; and
(d) in regard to a region where a shortage of exposure intensity arises, determining an auxiliary exposure dose for supplementing the shortage.
With this configuration, by using a pattern whose accuracy is desired to improve as the representative pattern, size accuracy of a transferred pattern as a whole can be improved in comparison with the prior art.
In the step (a), for example, an isolated rectangular pattern having a minimum design width W0 is selected as the representative pattern, and by adjusting a slice level of a forward scattering intensity distribution of the representative pattern such that a width of the distribution at the slice level becomes a design width W0, the slice level is determined as the reference exposure intensity Eth.
Since the isolated pattern receives no influence of backscattering, a relation of the slice level=the reference exposure intensity (a threshold value for developing) is not affected by processing of the steps (b) to (d). Especially, if the isolated pattern has the minimum width, a variation in width of a transferred pattern image for a small width pattern decreases in comparison with a variation in exposure condition for the same, thereby enabling to improve size accuracy of the transferred pattern image as a whole.
In still another aspect of the present invention, there is provided a charged particle beam exposure method in which plurality of patterns are collectively exposed by a charged particle projection method, comprising the steps of:
(a) irradiating a main exposure mask on which the plurality of patterns are formed with a charged particle beam to collectively expose a sensitive substrate; and
(b) irradiating an auxiliary exposure mask on which a pattern for performing auxiliary exposure in a region falling short of exposure intensity after the collective exposure is formed with a charged particle beam to collectively expose the sensitive substrate.
Since a large region can be collectively subjected to auxiliary exposure similarly to the main exposure mask, a throughput in exposure process increases.
According to another aspect of the present invention, there is provided with a rectangle/lattice data conversion method for a charged particle beam exposure mask pattern that, when a rectangular pattern or a rectangle of part thereof is actually or imaginarily formed as a first rectangular pattern on a sensitive substrate by charged particle beam exposure, converts a second rectangular pattern on a mask corresponding to said first rectangular pattern to a lattice pattern including plural pattern subshapes in order to reduce an exposure dose, wherein if a width of a pattern subshape is W, a space width between pattern subshapes is S, an area density of a lattice pattern is xcex1p, the minimum value of a forward scattering intensity in the first rectangular pattern is Ffminxc3x97xcex1p and a position assuming the minimum value is P, the method comprises the steps of:
(a) obtaining a function D(W, S) representing said area density xcex1p on the basis of a geometric relation of said lattice pattern, and obtaining a function E(P: W, S) representing a forward scattering intensity at said position P by surface-integration of a forward scattering term of an energy intensity distribution function, and
(b) obtaining said pattern subshape width W and said space width S satisfying relations D(W, S)=xcex1p and E(P: W, S)=Ffminxc3x97xcex1p, given both of an area density xcex1p and a forward scattering intensity reduction ratio Ffmin.
With this configuration, in a case where obtained values of pattern subshape width W and space width S are larger than respective allowable lower limits, size accuracy of a mask pattern can be secured without generating an exposure-short region. Further, calculation formulae for a pattern subshape width W and a space width S are given, and therefore in a case where values of an obtained pattern subshape width W and an obtained space width S are smaller than respective allowable lower limits, size accuracy of a mask pattern can be secured without generating an exposure-short region by altering shapes of pattern subshapes of a lattice pattern such that values of a to-be-obtained pattern subshape width W and a to-be-obtained space width S are larger than the respective allowable lower limits.
Further, according to another aspect of the present invention, there is provided with a rectangular pattern or a rectangle of part thereof is actually or imaginarily formed as a first rectangular pattern on a sensitive substrate by charged particle beam exposure, converts a second rectangular pattern on a mask corresponding to said first rectangular patter to a lattice pattern including plural pattern subshapes in order to reduce an exposure dose, wherein if a width of a pattern subshape is W, a space width between pattern subshapes is S, an area density of said lattice pattern is xcex1p, the minimum value of a forward scattering intensity in said first rectangular pattern is Ffminxc3x97xcex1p, and a position assuming the minimum value is P, the method comprises the steps of:
(a) obtaining a function D(W, S) representing said area density xcex1p on the basis of a geometric relation of said lattice pattern, and obtaining a function E(P: W, S) representing a forward scattering intensity at said position P by surface-integration of a forward scattering term of an energy intensity distribution function, and
(b) determining values of said pattern subshape width W and said space width S on the basis of said function D(W, S)=xcex1p, and values of said pattern subshape width W and said space width S or a value of a relation formula of S and W, given all of an area density xcex1p, an allowable lower limit Ffmin of a forward scattering intensity reduction ratio Ffmin, a common allowable lower limit value Lmin of both said pattern subshape width W and said space width S, and the values of said pattern subshape width W and said space width S or the value of the relation formula of S and W, and
(c) adopting the values of said pattern subshape width W and said space width S as parameters to determine said lattice pattern in a case where a condition is satisfied that Wxe2x89xa7Lmin, S xe2x89xa7Lmin and E(P: W, S)=Ffminxc3x97xcex1p.
With this configuration, the pattern subshape width W and the space width S can be determined by simpler calculation as well as the above-mentioned advantage is obtained.
According to another aspect of the present invention, there is provided with a rectangle/lattice data conversion method for a charged particle beam exposure mask pattern that, when a rectangular pattern or a rectangle of part thereof is actually or imaginarily formed as a first rectangular pattern on a sensitive substrate by charged particle beam exposure, converts a second rectangular pattern on a mask corresponding to said first rectangular pattern to a first lattice pattern in order to reduce an exposure dose, comprising the steps of:
(a) dividing said second rectangular pattern into plural rectangular regions;
(b) grouping said plural rectangular regions such that adjacent rectangular regions are included into first and second complementary patterns, respectively, complementary to each other in order to form said first lattice pattern using two masks complementary to each other;
(c) converting each of said plural rectangular regions to a second lattice pattern; and
(d) performing a boundary processing on each of said second lattice patterns such that at least one side of each peripheral subshape thereof is in contact with a side of a rectangular region corresponding to each of the second lattice patterns.
With this configuration, since a boundary processing is performed on a lattice pattern in each of rectangular regions, pattern subshapes are connected on both sides of a parting line, whereby even if a relative shift in position occurs when masks complementary to each other are interchanged therebetween in exposure operation, shortage of exposure due to increase in space width can be avoided.